a. ) 2x+3y = 23, 5x-20 = 8y
solve these by elimination method
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a. ) 2x+3y = 23, 5x-20 = 8y
solve these by elimination method
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Answer:
2x+3y=23
2x= 23-3y
x=(23-3y)/2----- put value of x in second equation
5(23-3y)-20= 8y
115-15y-20= 8y
95=23y
y= 95/23---- put in any equation
2x+2×95/23=23
2x+190/23=23
2x= 23-190/23
2x= 529-190/23
x= 339/46
Verified answer
[tex] \bf \purple{Question:}[/tex]
Solve linear equations 2x+3y=23 and 5x-20=8y using Elimination Method ?
[tex] \bf \purple{Answer:}[/tex]
[tex] \tt{\therefore \: x \: = \: \frac{244}{31} \: and \: y \: = \: \frac{75}{31} }[/tex]
[tex] \bf \purple{Step-by-step \: \: explanation:}[/tex]
Solution:
[tex] \tt{2x \: + \: 3y \: = \: 23}[/tex]
[tex] \tt{and \: \: 5x \: - \: 20 \: = \: 8y}[/tex]
[tex] \tt \: \: \: \: \therefore \: 5x \: - \: 8y \: = \: 20[/tex]
[tex] \tt{2x \: + \: 3y \: = \: 23 \: \Longrightarrow \: (1)}[/tex]
[tex] \tt{5x \: - \: 8y \: = \: 20\: \Longrightarrow \: (2)}[/tex]
[tex] \tt{equation(1) \: \times \: 5 \: \Longrightarrow \: 10x \: + \: 15y \: = \: 115}[/tex]
[tex] \tt{equation(2) \: \times \: 2 \: \Longrightarrow \: 10x \: + \: 16y \: = \: 40}[/tex]
[tex] \tt{Subtracting \: \Longrightarrow \: 31y \: = \: 75}[/tex]
[tex] \tt{\Longrightarrow \:y \: = \: \frac{75}{31} }[/tex]
[tex] \tt{Putting \: y \: = \: \frac{75}{31} \: in \: equation \: (1) \: , \: we \: have}[/tex]
[tex]2x \: + \:3 \bigg( \frac{75}{31} \bigg) \: = \: 23[/tex]
[tex] \Longrightarrow \: 2x \: = \bigg( \frac{225}{31} \bigg)[/tex]
[tex] \tt{ \Longrightarrow \: 2x \: = \frac{713 \: - \: 225}{31} }[/tex]
[tex] \tt{ \Longrightarrow \: 2x \: = \frac{448}{31} }[/tex]
[tex] \tt{ \Longrightarrow \: x \: = \frac{244}{31} }[/tex]
[tex] \bf{\therefore \: x \: = \: \frac{244}{31} \: and \: y \: = \: \frac{75}{31} } \: \red{ \underline{ \pink{Ans}}}[/tex]
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